噪声依赖状态和控制的时滞非线性随机系统Nash微分博弈

摘要

研究了一类噪声依赖于状态和控制的时滞非线性随机系统的2人Nash微分博弈问题,借助4个耦合的Hamilton-Jacobi方程组(HJEs)得到了Nash均衡策略存在的充分条件,即耦合HJEs如果存在解,Nash均衡策略就存在.同时给出了Nash均衡策略的显式表达.最后,通过一个数值算例验证了文中所得结论的有效性.%The problem of two-person Nash differential games for delayed nonlinear stochastic systems with state-and control-dependent noise is discussed. A sufficient condition for the existence of the Nash equilibrium strategy is presented in terms of coupled Hamilton-Jacobi equations (HJEs). And meanwhile, the explicit expression of the equilibrium strategy is given. In the end, a numeric example is employed to show the effectiveness of the obtained results.